23. In a right triangle ABC, 2B = 90, AB = 3cm and AC = 2V3cm. find 2C and ZA
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Answer:
GivenInRighttriangleABC,∠=90°
AB = 3\:cm , \: AC = 6\:cmAB=3cm,AC=6cm
\begin{gathered}i) sin \angle C = \frac{AB}{AC}\\= \frac{3}{6}=\frac{1}{2}\end{gathered}
i)sin∠C=
AC
AB
=
6
3
=
2
1
\implies sin\angle C = sin \:30\degree⟹sin∠C=sin30°
\implies \angle C = 30\degree⟹∠C=30°
\begin{gathered}ii) cos\angle A = \frac{AB}{AC}\\= \frac{3}{6}\\= \frac{1}{2}\end{gathered}
ii)cos∠A=
AC
AB
=
6
3
=
2
1
\implies cos \angle A = cos \:60\degree⟹cos∠A=cos60°
\implies \angle A = 60\degree⟹∠A=60°
Therefore.,
\red { \angle A}\green {= 60\degree }∠A=60°
\red { \angle C}\blue {= 30\degree }∠C=30°
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